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Abstract
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Let
be a
polynomially bounded o-minimal theory extending the theory of real closed ordered fields. Let
be a model of
equipped with a
-convex valuation
ring and a
-derivation.
If this derivation is continuous with respect to the valuation topology, then we call
a
-convex
-differential field. We
show that every
-convex
-differential field has an
immediate strict
-convex
-differential
field extension which is spherically complete. In some important cases, the
assumption of polynomial boundedness can be relaxed to power boundedness.
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Keywords
o-minimality, spherical completeness, valued differential
fields
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Mathematical Subject Classification
Primary: 03C64
Secondary: 12H05, 12J10
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Milestones
Received: 21 April 2021
Revised: 27 July 2022
Accepted: 27 September 2022
Published: 15 February 2023
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